Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
352 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×#901 | C2 | semidirect |
| 2. C3×#63464 | C2 | semidirect |
| 4. #11720538 | C2 | semidirect |
| 5. #11720300 | C2 | semidirect |
| 6. #11720291 | C2 | semidirect |
| 7. #11720286 | C2 | semidirect |
| 21. #88427 | C4 | semidirect |
| 22. #88425 | C4 | semidirect |
| 23. #88423 | C4 | semidirect |
| 24. #88421 | C4 | semidirect |
| 34. #63464 | D3 | semidirect |
| 104. #901 | D9 | semidirect |
| 217. C3×C9 | #444 | semidirect |
| 303. C9 | #5145 | semidirect |
| 339. C3 | #10588825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#901 | 2 |
| C3×#63464 | 2 |
| #11720881 | 2 |
| #11720538 | 2 |
| #11720300 | 2 |
| #11720291 | 2 |
| #11720286 | 2 |
| #10590922 | 3 |
| #10588825 | 3 |